Properties

Label 32192k
Number of curves $1$
Conductor $32192$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 32192k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32192.n1 32192k1 \([0, -1, 0, 319, 193]\) \(13651919/8048\) \(-2109734912\) \([]\) \(18432\) \(0.47852\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32192k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 32192k do not have complex multiplication.

Modular form 32192.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{5} + q^{7} - 2 q^{9} + 3 q^{11} + 3 q^{13} - 4 q^{15} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display